An Application of Mathematical Programming

The problem of sample allocation in multipurpose surveys is complicated by the fact that an efficient allocation for some estimates may be inefficient for others. There may also be precision goals that must be met for certain estimates plus constraints on costs and minimum sample sizes for strata to permit variance estimation. These requirements lead to formulating the allocation problem as one of mathematical programming with an objective function and constraints that are nonlinear in the sample size target variables. We discuss a flexible approach for a two-stage sample allocation that uses multicriteria optimization programming. Software was developed to permit survey designers to easily explore alternative problem formulations and to compare the resulting allocations. The method is illustrated using a business establishment survey that estimates the costs to employers of providing wages and benefits to employees and the percentages of employees that receive certain benefits.